Schultz' breakthrough role was the mentally unstable Captain "Howling Mad" Murdock on The A-Team. At the series outset, the producers felt that his character would be too over-the-top for viewers and planned to drop him after his debut, but early test screenings showed that he was popular with the audience. As a result, he was effectively "written back in" to the series.

Schultz has also appeared in films including The Fan (1981), as Broadway actress Lauren Bacall's director, and Fat Man and Little Boy (1989), as J. Robert Oppenheimer. During the filming of Fat Man and Little Boy he was frequently at odds with co-star Paul Newman. Newman was a liberal Democrat who favored nuclear disarmament, while Schultz is a conservative Republican, who opposed disarming.

In the early 1990s, he had a recurring role as Lieutenant Reginald Barclay in Star Trek: The Next Generation. Schultz reprised the role for Star Trek: Voyager and the film Star Trek: First Contact.Schultz is also known for his voice talent. His voice credits include numerous popular video games and cartoons.

He also is the host of a conservative talk radio podcast called Howling Mad Radio, which took a short hiatus until March 2009.